A transformation for transforming a first image given in polar coordinates into a second image given in Cartesian coordinates is particularly used for transforming a radar scan comprising radially scanned data, to be displayed on a regular (Cartesian) screen.
A radar scan system receives a plurality of pixels given in polar coordinates. Thus, the position of each data point is defined by an angle φi and a radius ri. Each so defined data point comprises additionally data as color and brightness. This additional data can also be zero, indicating, that for the corresponding data point no object was scanned. But usually, all pixels comprise any additional data, since areas or points where no objects were scanned might be indicated by a background color and brightness. It is also very common, to have information representing a noise of the radar scan. A plurality of such pixels forms a first image, even though this plurality of pixels might not be displayed to this end.
For displaying this plurality of pixels or for executing any computation or analysis on this pixels a transformation into Cartesian coordinates is desirable. This desire is also grounded on the fact, that most common computation programs for graphics are based on graphics given in Cartesian coordinates. In particular, most display systems like computer screens driven by a graphics card are based on Cartesian coordinates, and thus the position of each pixel on the screen is defined by Cartesian coordinates xi, yi.
One way of transforming radar scan data received in polar coordinates into Cartesian coordinates for displaying is disclosed in the WO 2004/015442. This document is incorporated in the present disclosure by reference. For transforming the radar scan image or video, data of a radar scan is received by a radar antenna or receiver and from there transmitted to a radar data receiver. The received digitized radar data is directly stored into a memory (polar store). The stored radar data usually comprises an angle of the radar antenna and distance from the radar antenna as a position information for each pixel. Additionally at least one information which is e.g., representative for the intensity value of each pixel is stored with the data defining the position of the pixel. For transforming the stored radar data into an image defined by Cartesian coordinates x, y a transformation is basically transformed for each pixel. Therefore, for the Cartesian coordinates xi, yi the respective polar coordinates ri, φi are determined. For each thus determined polar coordinates ri, φi the corresponding information (e.g., the intensity value) is searched in the polar store of the memory where the radar data is stored and this information is transferred and allocated to the corresponding pixel of the image given in Cartesian coordinates. This method is also called reverse scan conversion. For displaying the intensity value of the corresponding pixel might be transformed into a color, which corresponds to the corresponding intensity value according to a certain standard.
Often, the polar coordinates corresponding to the Cartesian coordinates are determined by reading them out of a look up table. For transforming, the corresponding polar coordinates must be received from this look up table for each Cartesian coordinates and thus for each pixel. Other methods may calculate the polar coordinates ri, φi.
The above described method has the disadvantage, that calculating the polar coordinates for each pixel or using a look up table to read out the polar coordinates for each pixel is very time consuming. Thus, using micro processors which are available nowadays it is a problem, to transform a radar scan image of regular size into an image given in Cartesian coordinates in real time. Also, executing this complex computations or accessing the look up table consumes a large amount of processor capacity. Often, look-up tables must be recalculated e.g., when a zoom-operation is performed, thus disabling the radar scan converter during the recalculation process. Thus, a powerful processor is needed to execute the transformation, which increases hardware costs. Additionally, only few capacity of the employed processor is leftover and thus available for additional jobs as controlling further input or output functions or running further applications on the processors.
Since known transformation techniques are quite time consuming it is also a problem, to display one or more radar scan images or videos of one or more radar antennas and possibly additional geographical data in one display plane. According to the state of the art radar scan images and videos and geographical data received from different display planes are displayed on one display by just shifting, rotating or zooming each image, not considering each geographical projection, thus resulting in distortions and discrepancies of the images.